loglogistic2_gradient {drda}

2-parameter log-logistic function gradient and Hessian

Description

Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter log-logistic function.

Usage

loglogistic2_gradient(x, theta, delta)

loglogistic2_hessian(x, theta, delta)

loglogistic2_gradient_hessian(x, theta, delta)

Arguments

x

numeric vector at which the function is to be evaluated.

theta

numeric vector with the two parameters in the form c(eta, phi).

delta

value of delta parameter (either 1 or -1).

Details

The 2-parameter log-logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = x^eta / (x^eta + phi^eta)⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

where x >= 0, theta = c(alpha, delta, eta, phi), eta > 0, and phi > 0. Only eta and phi are free to vary (therefore the name), while c(alpha, delta) are constrained to be either c(0, 1) (monotonically increasing curve) or c(1, -1) (monotonically decreasing curve).

Value

Gradient or Hessian evaluated at the specified point.